量子基礎・量子情報の新展開

I present an entropic uncertainty relation for arbitrary quantum states and POVMs derived from a retrodictive formulation of quantum measurement. The construction assigns to each measurement outcome a canonical retrodictive state, enabling a symmetric joint probability distribution for pairs of measurements and a measure of mutual retrodictability. The resulting uncertainty bound has the standard operational meaning in terms of measurement statistics and further connects entropic uncertainty to approximate recoverability and Groenewold-Ozawa information gain. Numerical comparisons show that this retrodictive uncertainty relation can outperform standard entropic bounds for broad classes of states and measurements.